Problem: Simplify the following expression: $ r = \dfrac{7}{4} + \dfrac{7q + 1}{-3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3}{-3}$ $ \dfrac{7}{4} \times \dfrac{-3}{-3} = \dfrac{-21}{-12} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{7q + 1}{-3} \times \dfrac{4}{4} = \dfrac{28q + 4}{-12} $ Therefore $ r = \dfrac{-21}{-12} + \dfrac{28q + 4}{-12} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-21 + 28q + 4}{-12} $ $r = \dfrac{28q - 17}{-12}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{-28q + 17}{12}$